I put my JLX Soft top Vitara across the Wollondilly river, at the nudist resort, and the water, was over my bonnet, and 4 inches up my windows, yes got some water in the back, but I had no snorkel, the back wheels were floating, and luckiiy in 4 wd the front wheels were touching the boulders in the water, due to engine weight, and managed to cross this river, in those conditions, 3 times in the same day. I got no water, in thru the air intake, nor into the engine. My later Vitara a 2001 mod, was set up better for water crossings but it also didn't have a snorkel, and did drive with water over the bonnet on numerous times, and also had the diff breathers, set up from factory, with the extend lines, and had one way valves, on the end of those lines, that let the air out but not water in. Those lines where on the diffs, the transmission, and the transfer case. Never should have sold that vitara, but the daughter wanted it badly to set up for serious off roading, so parted with it.

Ok wheres the std air filter ? If it is under your bonnet your lucky . If water is ingested ? Big chance your up for new connecting rods / another engine ! . Water does NOT compress !! No matter what make it is !! More so on Diesel engines too !!

Bow waves do make a picture look good. Problem is the vehicles start to float if they get too deep, and then the occupants are in trouble. I haven't been in that situation, always walked the road first. But why wreck your vehicle just to make a good picture. The advise I got was to remove the doors before doing a deep crossing.

The more colder, denser the air is makes more difference than air pressure !! Although it all helps

Most 4x4 unladen will become too buoyant to maintain traction in still water at a depth of around 900mm, but most 4x4 air filter intakes are mounted at around 500-600mm.

So, protecting the air filter/intake with cleaner air on dirt roads, and dry air on water crossings are the primary reasons for a snorkel.

Oh, and if the water is flowing moderately in a stream or crossing deeper than around 400mm and you're not carrying some decent weight on board, you're going to get washed off that causeway, snorkel or no snorkel.